1. Field of the Invention
This invention is generally concerned with magnetic resonance imaging (MRI) and, more particularly, to the formation of gradient fields in an imaging volume.
2. Description of the Prior Art
A prior art MRI apparatus, such as that depicted in FIG. 1 and disclosed in U.S. Pat. No. 4,952,878, which is hereby incorporated by reference, is comprised of a magnet system 2 and a magnet supply source 6 for generating a homogeneous stationary magnetic field H.sub.o. A magnet system 4 and a supply source 8 generate magnetic gradient fields and an RF coil 10, connected to an RF amplifier 12, generates a radio frequency alternating magnetic field.
The uniform magnetic field H.sub.o produced by the magnet system 2 and the magnet supply source 6 is formed within an imaging volume along a z axis and causes the nuclei within the object to tend to be aligned along the z axis. The nuclei precess about the z axis at their Larmor frequencies according to the following equation: EQU .omega..sub.o =.gamma.H.sub.o EQ. ( 1)
where .omega..sub.o is the Larmor frequency at a field strength of H.sub.o and .gamma. is the gyromagnetic ratio. The gyromagnetic ratio .gamma. is a constant and is a property of the particular subatomic particle. For instance, the gyromagnetic ratio .gamma. for water protons is 4.26 kHz/gauss. Thus, in a 1.5 Tesla polarizing magnetic field H.sub.o, the resonant or Larmor frequency of water protons is approximately 63.9 MHz.
In a typical imaging sequence, the RF coils 10 are used to generate an RF signal centered at the Larmor frequency .omega..sub.o. In conjunction with this RF signal, a magnetic field gradient G.sub.z is generated with the gradient coils 4 so that only the nuclei in a selected slice through the object along the x-y plane, which have a resonant frequency centered at the Larmor frequency .omega..sub.o, are excited and absorb energy. Next, the gradient coils 4 are used to produce magnetic field gradients along the x and y axes. Generally speaking, the x axis gradient G.sub.x spatially encodes the precessing nuclei continuously by frequency and the y axis gradient G.sub.y is used to pulse phase encode the nuclei.
The RF coils 10 may be formed in the design of a "bird cage" or a "squirrel cage" as shown in FIG. 2. Other RF coil designs are also known, such as those disclosed in U.S. Pat. No. 4,717,881, U.S. Pat. No. 4,757,290, U.S. Pat. No. 4,833,409, U.S. Pat. No. 4,916,418, U.S. Pat. No. 5,017,872, U.S. Pat. No. 5,041,790, U.S. Pat. No. 5,057,778, and U.S. Pat. No. 5,081,418. The RF coils 10 generate a circularly polarized RF field which rotates near the Larmor frequency over the antenna wires 30 of the coil. The RF coils 10 are also used to detect signals from the object and to pass the detected signals onto a signal amplifier 14, a phase-sensitive rectifier 16, and to a control device 18.
A description of the above process is given in more detail below. The spins of the nuclei have an angular momentum S which is related to their magnetic moment .mu. through the gyromagnetic ratio .gamma., by the equation: EQU .mu.=.gamma.S EQ. (2)
With reference to FIG. 3, a single nucleus 1 has a magnetic moment 3. All of the spins are subjected to a total ambient magnetic field H defined by the equation: EQU H=ih.sub.x +jh.sub.y +k(H.sub.o +h.sub.z) EQ. (3)
As a result of the total magnetic field H, a torque T is produced on each spin. With reference to FIG. 3, the total magnetic field H produces a torque T on the nucleus 1 to cause the nuclei 1 to precess. The torque T produced is defined by the following equation: ##EQU1## Substituting and rearranging from the above equations yields: ##EQU2## From equation (6), it is evident that the differential spatial phase increment d.PHI. of each spin is related to a cross product of the direction of each spin .PHI. with the ambient magnetic field H multiplied by the gyromagnetic constant .gamma..
Substituting from the above equations yields: EQU D.PHI.=(.PHI..times..gamma.(ih.sub.x +jh.sub.y))dt+(.PHI..times..gamma.k(H.sub.o +h.sub.z))dt EQ. (7)
or EQU d.PHI. d.theta.+d.phi. EQ. (8)
where d.theta. is the differential increment of spatial phase of the precession of .mu. about an axis perpendicular to the z axis and d.phi. is the differential increment of the spatial phase of the precession of .mu. about the z axis 7. Therefore, the time-varying angular relationship of each magnetic moment .mu. is controlled by the applied ambient magnetic field H.
A differential increment d.theta. of .mu. is produced when ih.sub.x +jh.sub.y rotates synchronously with .phi. at the Larmor frequency. Often, the RF coils 10 are used to create such a circularly polarized RF magnetic field which rotates at the Larmor frequency .omega..sub.o by selectively choosing the values of ih.sub.x +jh.sub.y. As a result, an interaction energy W.sub.m is transferred to the spins and is given by: EQU dW.sub.m =-T.multidot.d.theta.=-(.mu..times.k(H.sub.o +h.sub.z)).multidot.d.theta. EQ. (9) EQU W.sub.m =.mu.(H.sub.o +h.sub.z) (cos.theta.-1) EQ. (10)
If the spins are coupled to the surrounding medium to permit relaxation to the minimum energy W.sub.m state before the application of ih.sub.x +jh.sub.y, then the average value of .theta. for a discrete volume of spins will be at a minimum. The vector sum of each of the magnetic moments .mu. in a discrete volume will then produce a net magnetization M aligned with the z axis. The precessions of the spins .theta. produced by ih.sub.x +jh.sub.y about an axis perpendicular to the z axis will give the net magnetization M a transverse component M.sub.T with a spatial phase .phi.. The strength of the transverse magnetization M.sub.T is a function of the number of spins in each discrete sample volume and of the previous excitation and relaxation history of these spins. The transverse magnetization M.sub.T is a component of the intensity of a total rotating flux density B.sub.T through the permeability of free space .mu..sub.o where: EQU B.sub.T =.mu..sub.o (ih.sub.x +jh.sub.y +M.sub.T) EQ. (11)
If an antenna loop is placed with its area vector perpendicular to the z axis, it will have a voltage induced in it which is proportional to the time derivative of B.sub.T and also a function of the geometry of the conducting antenna loop and of the spatial distribution of the discrete sample volumes, each containing a singular value of B.sub.t. This functional dependance is given by the Maxwell-Faraday equation and the vector reception field of the antenna geometry, which may be determined by experimentation.
The transverse magnetization M.sub.T has an instantaneous rotational frequency: ##EQU3##
A polar vector field G is defined as the gradient of h.sub.z and is determined according to the following equation: ##EQU4## As discussed above with reference to FIG. 1, the gradient magnets 4, or other type of "gradient coils," provide a spatial address for each discrete component of the imaging volume. The polar vector field G, having components G.sub.x, G.sub.y, and G.sub.z defined by Equation 14, is successively incremented by driving the gradient coils over a longer pulse interval or by incrementing the amplitude of the driving current. The signal from the imaging volume is analyzed by Fourier transformation or other integral transformation, to produce a mathematical representation of the spatial address of the transverse magnetization M.sub.T in the complex plane.
A problem with many prior art MRI systems, however, is that the time needed to produce the image is relatively long, for instance about 6 minutes. During this time the object to be imaged, for instance the patient, must remain motionless.
The prior art MRI systems are also at a disadvantage due to the manner in which gradient fields are produced. Gradient field generating systems, such as the supply system 8 and the gradient magnet system 4 of FIG. 1, must be able to quickly pulse large currents while precisely controlling the magnitudes of these currents. The pulsing of the large currents produces a pounding noise which often times must be blocked out with earplugs. Although many types of MRI pulse sequences can help reduce the time needed to scan an image, the circuitry in these supply systems becomes extremely complex as well as very costly, in order to provide precise control of large currents.
An additional problem with many MRI systems is that they are unable to generate rotating gradient fields that are sufficiently linear for projection reconstruction image acquisition techniques. Thus, these MRI systems are incapable of producing images by techniques such as projection reconstruction, but must instead rely upon a two or three dimensional truncated Fourier series and the Fourier transformation to produce an image.
The prior art MRI systems further suffer from a disadvantage in that the gradient fields are only produced to a first order approximation of the desired linear gradient fields. Because the gradient fields produced only approximate the desired linear fields, some of the image reconstruction systems used in the prior art systems suffered as a result.